Interior control of waves on time dependent domains

TL;DR

This paper establishes new interior control results for wave equations on domains that change over time, using advanced Carleman estimates and observability inequalities without requiring time analyticity.

Contribution

It introduces a novel approach to control wave equations on dynamic domains, improving control regions beyond standard methods without assuming time analyticity.

Findings

Derived a new Carleman estimate for time-dependent domains

Proved an observability inequality for wave equations on moving domains

Achieved improved control regions compared to traditional methods

Abstract

We obtain a novel interior control result for wave equations on time dependent domains. This is done by deriving a suitable Carleman estimate and proving the corresponding observability inequality. We consider the wave equation with time dependent lower order coefficients, without any time analyticity assumptions. Moreover, we obtain improved control regions when compared with standard Carleman methods.